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its transmission from the moving to the working points ; and all the 
rest is accumulated or treasured up in the moving parts of the ma- 
chine, and is reproducible whenever the work of the moving power 
from exceeding shall fall short of that which must be expended upon 
the useful and the prejudicial resistances to carry on the machine. 
He then proceeds to observe, that in every machine there thus 
exists a direct relation between these four elements, — the work done 
upon the moving points, that expended at the working points, that 
expended on the prejudicial resistances, and that accumulated in the 
moving elements. This relation, which is always the same for the 
same machine, and different for different machines, he proposes to 
call, in respect to each particular machine, its modulus ; and he states 
the principal object of this paper (and of another whicli he proposes 
subsequently to submit to the Society) to be, first, the general de- 
termination of the modulus of a simple machine ; secondly, that of 
a compound machine, from a knowledge of the moduli of its compo- 
nent elements ; and, thirdly, the application of these general methods 
of determination to some of the principal elements of machinery, and 
to the machines which are in common use. 
The author then states, that the velocities of the different parts, or 
elements of every machine are connected with one another by certain 
invariable relations, capable of being expressed by mathematical for- 
mulae ; so that, though these relations are different for different ma- 
chines, they are the same for the same machine. Thus it becomes 
possible to express the velocity of any element of a machine, at any 
period of its motion, in terms of the corresponding velocity of any 
other element. Whence it results that the whole vis viva of the 
machine may at any time be expressed in terms of the corresponding 
velocity of its moving point (that is, the point where the moving 
power is applied to it), and made to present itself under the form V* 
2 o) \ 2 , where V represents the velocity of the moving point of the 
machine, oj the weight of any element, and X a factor determining 
the velocity of that element in terms of the velocity V of the moving 
point. Substituting this expression for the vis viva or accumulated 
work in the modulus and solving in respect to V, an expression is 
obtained, whence it becomes apparent that the variation of the velo- 
city V of the moving point, produced by any given irregularity in 
the work done upon the moving or working points, will be less, as 
the factor 2 w X- is greater. This factor, determinable in eveiy ma- 
chine, and upon which the uniformity of its action under given 
variations of the power which impels it depends, he proposes to in- 
troduce into the general discussion of the theory of machines as the 
coefficient of equable motion. 
He then proceeds to investigate general methods for the determina- 
tion of the modulus of a machine, deducing them from those general 
relations which are established by the principles of statics, between 
the pressures applied to the machine, in its state bordering upon 
motion. 
That he may escape that complication of formulae which results 
from the introduction of friction, by the ordinary methods, into the 
